Use this seismology calculation to reproduce a stated convention, screen observations, or compare scenarios whose units, coordinate conventions, catalog selection, and model assumptions are known.

TR (yr)

Required number in yr. Mean return period.

T (yr)

Required number in yr. Exposure window.

The cited overview of Seismology supplies background for the terminology and domain context used by this tool.^[1]

Probability of at least one exceedance within T years for a Poisson process: P = 1 − exp(−T/TR). Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

P (%)

Returned number in %. Exceedance probability.

λ (1/yr)

Returned number in 1/yr. Equivalent annual rate.

• Earth structure, source geometry, path effects, site response, instrument response, catalog completeness, uncertainty, and the fitted range can dominate the accuracy of simplified seismic calculations.
• TR must be at least 0.
• T must be at least 0.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

For analysis or hazard decisions, retain uncertainty and provenance and compare the result with waveform processing, calibrated regional models, and guidance from qualified seismologists or the responsible agency.

• Annual Rate To T Years Exceedance Converter

  Convert an annual exceedance rate to the probability of exceeding at least once in T years.

• Event Count Poisson Confidence Interval Gehrels Approximation

  Gehrels (1986) algebraic approximations to the 84.13% one-sided Poisson limits (the conventional asymmetric one-sigma error bars), including the tabulated 1.841 upper limit for zero counts.

• Directivity Narrowband Pulse Period Calculator

  First-order rupture-duration proxy for directivity pulse period: T_p ≈ L/v_r.